“Before British producer Andy Sneap entered the studio with the heavy-metal band Accept, he made the German rockers listen to their own classic records from the ’80s. Mr. Sneap, one of metal’s most in-demand producers, singled out the chant-like background vocals he considered core to Accept’s DNA. He “told us to be more German,” Accept’s 58-year-old guitarist Wolf Hoffmann says. “We initially didn’t even know—what the hell is that?”

Four successful Accept studio albums later, Mr. Sneap has carved out a niche by helping other metal veterans such as Judas Priest, Saxon and Megadeth revive their youthful sound without lapsing into nostalgia. Mr. Sneap, who is 49, fits neither the mold of the musical Svengali nor the bottom-line-obsessed A&R executive. Instead, he uses his intuition as a fan to remind older bands why listeners love them.”

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“In the 1980s, we really didn’t want to sound German at all,” Mr. Hoffmann says. Accept’s 2010 album, “Blood of the Nations,” was a success, metal experts say. The group’s 2014 record, “Blind Rage,” became its highest-charting U.S. album.

“They nail the details. They double down on the essential twists that make Accept” special, says Mr. Schafer, the metal critic. “These are probably the best comeback records of any metal band.”

Mark Tornillo, left, and Wolf Hoffmann of the band Accept, at a show in February in Oslo, Norway. For the German heavy-metal group’s comeback albums, British producer Andy Sneap had them listen to their earlier songs and encouraged them to sound ‘more German.’ PHOTO: GONZALES /JAN-ERIK ERIKSEN/AVALON/ZUMA PRESS